Sorry, but this page and MATDS are under construction now!
MATDS is a MATLAB-based program for dynamical system investigation. It will be MATLAB-version of DESIR program. MATDS is a graphical MATLAB package for the interactive numerical study of dynamical systems. It works with version 6.5* of MATLAB. Now only ordinary differential equation study
Current version is 1.0 beta.
Author: Govorukhin V.N. E-Mail: vgov@math.rsu.ru, matds@nm.ru
To install the package you need make a MATDS directory, copy matds.zip-file to this directory and run unzip -a matds.zip. This creates a subdirectories of MATDS with all necessary files. MATDS directory must be added to MATLAB path or must be a current work directory for MATLAB. For start MATDS type matds in matlab main window.
MATDS directory structure:
TEMP - working directory for temporary files.
MATHS - directory for mathematical part of MATDS.
SYSTEMS - directory for dynamical systems files.
GUI - directory for GUI and service part of MATDS.
Example:
Information about current working status displays in main window.
Class - type of dynamical system.
System - name of system.
Fig.2. Main menu of MATDS |
(see Fig. 1)
Fig.3. 2D output window. |
Fig.4. 3D output window. |
Fig.5. Menu of the first step of system definition |
Fig.6. Window for system editing (second step of definition) |
In the program all standard methods of MATLAB ODE suite are included, and also additional means are used: integrators of high accuracy ode78 and ode87.
Fig.7. Chaotic trajectory in Chua system |
Fig.8. Trajectories in ABC-flow (ODE system with periodic right hand side) |
Some special integrators (simplectic, stiff etc.) will be added in next versions!
Fig.9. Tube plot corresponding to Lorenz attractor. |
Fig.10. Vector field and limit cycle |
Now only finding of equilibria and stability analysis for fixed value of parameter is possible in MATDS. Newton method used for equilibria finding. Current initial point (main menu -> Edit -> Initial point) is a initial condition for Newton method. Stable equilibria is depicted by green circle and ustable ones by red.
Examples:
Fig.11. Three unstable equilibria in Lorenz system. |
Continuation equilibria along parameters with elements of bifurcation analysis will be added in next versions!
Will be added in next versions...
Now exist two types of Poincare map in MATDS: Section by time (output points of trajectory with fixed time interval); Section by plane in phase space. Type of map and equation of plane or time interval can be defined in dialog window. For activate Poincare map calculation user must
Fig.12. Poincare map by time definition |
Fig.13. Poincare map by plane definition |
Fig.14. Two Poincare section and chaotic trajectory for ABC flow. |
Fig.15. Poincare map for Ueda attractor (by time). |
To activate Lyapunov exponents calculation user must call Research->Lyapunov
item in main MATDS menu. After that Number of exponents k (0<k<=dimension
of syste), step of averaging for algorithm (see, A. Wolf, J. B. Swift, H. L. Swinney, and J. A.
Vastano, "Determining Lyapunov Exponents from a Time Series," Physica D,
Vol. 16, pp. 285-317, 1985.) and step of values output must be defined.
Fig.16. Options menu for Lyapunov exponents calculation. |
Fig. 17. Lyapunov exponents for Lorenz system (value of parameters: R=28, b=8/3, sigma=10). |
Will be added in next versions...
Now MATDS is under construction and can be a bugs, sorry...
The author will be very grateful to any information on work of the program both any remarks and suggestions!
To download what you need, simply click on the appropriate links below. The file matds.zip contains the latest version of the package.
If you want to receive the information on MATDS and development of the program send E-Mail to author with subject MATDS.